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Product Code:  MMONO/184 
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eBook ISBN:  9781470445980 
Product Code:  MMONO/184.E 
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AMS Member Price:  $124.00 
Hardcover ISBN:  9780821810828 
eBook: ISBN:  9781470445980 
Product Code:  MMONO/184.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 
Hardcover ISBN:  9780821810828 
Product Code:  MMONO/184 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445980 
Product Code:  MMONO/184.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821810828 
eBook ISBN:  9781470445980 
Product Code:  MMONO/184.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 184; 1999; 133 ppMSC: Primary 90; Secondary 60
Financial mathematics is going through a period of intensive development, particularly in the area of stochastic analysis. This timely work presents a comprehensive, selfcontained introduction to stochastic financial mathematics. It is based on lectures given at Moscow State University, “Stochastic Analysis in Finance”, and comprises the basic methods and key results of the theory of derivative securities pricing in discrete financial markets.
The following elements: martingales, semimartingales, stochastic exponents, Itô's formula, Girsanov's theorem, and more, are used to characterize notions such as arbitrage and completeness of financial markets, fair price and hedging strategies for options, forward and futures pricing, and utility maximization. Limiting transition from a discrete to continuous model with derivation of the famous BlackScholes formula is shown.
The book contains a wide spectrum of material and can serve as a bridge to continuous models. It is suitable as a text for graduate and advanced graduate students studying economics and/or financial mathematics.
ReadershipGraduate students and researchers working in probability theory, stochastic processes, and financial mathematics.

Table of Contents

Chapters

Basic concepts and objects of a financial market

The elements of discrete stochastic analysis

A stochastic model for a financial market. Arbitrage and completeness

Pricing European options in complete markets. The binomial model and the CoxRossRubinstein formula

Pricing and hedging American options in complete markets

Financial computations on a complete market with the use of nonselffinancing strategies

Incomplete markets. Pricing of options and problems of minimizing risk

The structure of prices of other instruments of a financial market. Forwards, futures, bonds

The problem of optimal investment

The concept of continuous models. Limiting transitions from a discrete market to a continuous one. The BlackScholes formula

Appendix 1

Appendix 2

Appendix 3


Additional Material

Reviews

The book provides a rigorous, selfcontained and concise introduction to the rapidly developing field of mathematical finance. It may serve very well as a textbook for graduate students in mathematics or finance.
Mathematical Reviews 
The book is carefully written and contains a short but clear introduction to the theory of stochastic modelling of financial markets. It could be highly recommended as an introductory course to the topic for graduate students and specialists interested in financial mathematic problems.
Zentralblatt MATH


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Financial mathematics is going through a period of intensive development, particularly in the area of stochastic analysis. This timely work presents a comprehensive, selfcontained introduction to stochastic financial mathematics. It is based on lectures given at Moscow State University, “Stochastic Analysis in Finance”, and comprises the basic methods and key results of the theory of derivative securities pricing in discrete financial markets.
The following elements: martingales, semimartingales, stochastic exponents, Itô's formula, Girsanov's theorem, and more, are used to characterize notions such as arbitrage and completeness of financial markets, fair price and hedging strategies for options, forward and futures pricing, and utility maximization. Limiting transition from a discrete to continuous model with derivation of the famous BlackScholes formula is shown.
The book contains a wide spectrum of material and can serve as a bridge to continuous models. It is suitable as a text for graduate and advanced graduate students studying economics and/or financial mathematics.
Graduate students and researchers working in probability theory, stochastic processes, and financial mathematics.

Chapters

Basic concepts and objects of a financial market

The elements of discrete stochastic analysis

A stochastic model for a financial market. Arbitrage and completeness

Pricing European options in complete markets. The binomial model and the CoxRossRubinstein formula

Pricing and hedging American options in complete markets

Financial computations on a complete market with the use of nonselffinancing strategies

Incomplete markets. Pricing of options and problems of minimizing risk

The structure of prices of other instruments of a financial market. Forwards, futures, bonds

The problem of optimal investment

The concept of continuous models. Limiting transitions from a discrete market to a continuous one. The BlackScholes formula

Appendix 1

Appendix 2

Appendix 3

The book provides a rigorous, selfcontained and concise introduction to the rapidly developing field of mathematical finance. It may serve very well as a textbook for graduate students in mathematics or finance.
Mathematical Reviews 
The book is carefully written and contains a short but clear introduction to the theory of stochastic modelling of financial markets. It could be highly recommended as an introductory course to the topic for graduate students and specialists interested in financial mathematic problems.
Zentralblatt MATH